Neutrino Mass Sum Rules from Modular $\mathcal{A}_4$ Symmetry

TL;DR

This paper introduces a minimalistic model using modular $ ext{A}_4$ symmetry within a type-II seesaw framework, deriving a neutrino mass sum rule that constrains the absolute neutrino mass scale and has testable cosmological implications.

Contribution

It presents a novel minimalistic model with modular $ ext{A}_4$ symmetry that predicts a specific neutrino mass sum rule linking oscillation data to absolute mass scale.

Findings

Predicts total neutrino mass sum around 0.1 eV for both mass orderings.

Provides a testable relation that constrains neutrino mass parameters.

Implications for cosmology and neutrinoless double beta decay experiments.

Abstract

Modular symmetries offer a dynamic approach to understanding the flavour structure of leptonic mixing. Using the modular $\mathcal{A}_4$ flavour symmetry integrated in a type-II seesaw, we propose a simple and minimalistic model that restricts the neutrino oscillation parameter space and, most importantly, introduces a sum rule in the physical neutrino masses. When combined with the mass squared differences observed in neutrino oscillations, this sum rule determines the absolute neutrino mass scale. This has significant implications for cosmology, neutrinoless double beta decay experiments and direct neutrino mass measurements. In particular, the model predicts $\sum_i m_i \approx 0.1$ eV for both normal and inverted ordering, and thus can be fully probed by the current generation of cosmological probes in the upcoming years.